Search results
Results from the WOW.Com Content Network
The hardest problems in PSPACE. PTAS: Polynomial-time approximation scheme (a subclass of APX). QIP: Solvable in polynomial time by a quantum interactive proof system. QMA: Quantum analog of NP. R: Solvable in a finite amount of time. RE: Problems to which we can answer "YES" in a finite amount of time, but a "NO" answer might never come. RL
NP and co-NP together form the first level in the polynomial hierarchy, higher only than P. NP is defined using only deterministic machines. If we permit the verifier to be probabilistic (this, however, is not necessarily a BPP machine [6]), we get the class MA solvable using an Arthur–Merlin protocol with no communication from Arthur to Merlin.
As it is suspected, but unproven, that P≠NP, it is unlikely that any polynomial-time algorithms for NP-hard problems exist. [3] [4] A simple example of an NP-hard problem is the subset sum problem. Informally, if H is NP-hard, then it is at least as difficult to solve as the problems in NP.
A problem is hard for a class of problems C if every problem in C can be polynomial-time reduced to . Thus no problem in C is harder than , since an algorithm for allows us to solve any problem in C with at most polynomial slowdown. Of particular importance, the set of problems that are hard for NP is called the set of NP-hard problems.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
In his 1994 book The Language Instinct, he wrote: The main lesson of thirty-five years of AI research is that the hard problems are easy and the easy problems are hard. The mental abilities of a four-year-old that we take for granted – recognizing a face, lifting a pencil, walking across a room, answering a question – in fact solve some of ...
The subset sum problem (SSP) is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle T} , and the question is to decide whether any subset of the integers sum to precisely T {\displaystyle T} . [ 1 ]
Problems 1, 2, 5, 6, [g] 9, 11, 12, 15, 21, and 22 have solutions that have partial acceptance, but there exists some controversy as to whether they resolve the problems. That leaves 8 (the Riemann hypothesis ), 13 and 16 [ h ] unresolved, and 4 and 23 as too vague to ever be described as solved.